Archives

Forcing Axioms and Ultimate L

Mathematics has a reputation for objectivity. But without real-world infinite objects upon which to base abstractions, mathematical truth becomes, to some extent, a matter of opinion — which is Simpson’s argument for keeping actual infinity out of mathematics altogether. The choice between V=ultimate L and Martin’s maximum is perhaps less of a true-false problem and more like asking which is lovelier, an English garden or a forest?

-Natalie Wolchover, “To Settle Infinity Dispute, a New Law of Logic”

Today, a little taste of contemporary set theory, the type of mathematics I actually work on. I point you towards Natalie Wolchover’s 2013 piece for Quanta Magazine about some recent work in set theory, particularly relating to the Continuum Hypothesis. The piece isn’t perfect, and certain things are a bit caricatured, but overall it’s pretty nice work.